Question

The instantaneous values of AC and AC source in a circuit are, $i=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)$ and $E=\frac{1}{\sqrt{2}}\sin (100\pi t+\pi /3)$ respectively. The average power consumed in the circuit is

• A. $\frac{1}{2}\text{W}$
• B. $\frac{1}{8}\text{W}$
• C. $\frac{1}{4}\text{W}$
• D. $\frac{1}{5}\text{W}$

Answer 1

The correct option is B $\frac{1}{8}\text{W}$

Given:

$i=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)$

$E=\frac{1}{\sqrt{2}}\sin (100\pi t+\pi /3)$

Here, the phase difference between the voltage and the current is, $\varphi =\pi /3$.

Now, average power,

$P_{\text{avg}}=E_{\text{rms}}{i}_{\text{rms}}\cos \varphi$

$\Rightarrow P_{\text{avg}}=\frac{E_0}{\sqrt{2}}\frac{i_0}{\sqrt{2}}\cos \varphi$

$\Rightarrow P_{\text{avg}}=\frac{1/\sqrt{2}}{\sqrt{2}}\times \frac{1/\sqrt{2}}{\sqrt{2}}\times \cos \left(\pi /3\right)=\frac{1}{8}\text{W}$

Hence, option $\left(B\right)$ is the correct answer.